Is math hard because we’re teaching it wrong?

Introducing concepts before equations may make it easier to learn math. (iStock)

For as long as there have been math worksheets and flashcards, children have learned the mechanics of solving equations before graduating to deeper mathematical concepts. It’s not uncommon for young students to labor over addition, subtraction, multiplication and division problems without having a firm grasp on the underlying concepts that make the equations work.

Peabody researcher Emily Fyfe taught 122 Nashville second and third graders the concept of math equivalence—the idea that two sides of an equation represent the same quantity. Half of the students received verbal instruction on math equivalence prior to being given problems to solve; the other half received instruction after doing the assignment. Both groups were asked to provide explanations of their process afterward.

“Children in Western countries often misinterpret the equal sign as an operator, meaning ‘get the answer,’ rather than as a relational symbol that indicates two equal amounts,” Fyfe said. “We wanted to see how providing an explanation of the concept first would affect the students’ accuracy on relevant problems.”

Children who were instructed on math equivalence before being asked to solve the equations had a 67 percent accuracy rate, as compared to just 44 percent in the other group. In addition, the children who learned the concept before solving were able to provide more clear explanations of math equivalence afterward.

“The results suggest there is a time for providing conceptual instruction before problem-solving, such as when it is an activity that activates and engages misconceptions,” Fyfe said.

Co-authors on the study were Marci S. DeCaro, department of psychological and brain sciences at University of Louisville; and Bethany Rittle-Johnson, associate professor psychology at Peabody College. The research was supported by the National Science Foundation and the U.S. Department of Education.

I’m not sure if you’re a teacher Jean, but teaching concepts first, or at least at the same time, has been round long enough now in many schools to have reached the inevitable part of the educational cycle that it’s been blamed now for all the kids that don’t know their times tables.

The trouble is of course that understanding the concept of multiplication doesn’t help me quickly recall what 7×6 is. As all things in education, balance between these seemingly opposing philosophies is best.

Georgene Troseth

Philip, I think the point is that children’s use of the equal sign involves a misconception. Memorizing times tables doesn’t. That’s why Emily is quoted as saying “there is a time for providing conceptual instruction before
problem-solving, such as when it is an activity that activates and
engages misconceptions.” Yay OUR Emily Fyfe!